Ingrid Stairs UBC

Rencontres de Moriond La Thuile

March 25, 2011

General Relativity Tests with Pulsars

Green Bank Telescope

Parkes Arecibo

Jodrell Bank

Outline

•  Intro to pulsar timing •  Equivalence principle tests - “Nordtvedt”-type tests - Orbital decay tests •  Relativistic systems - Timing - Geodetic precession - Preferred-frame effects •  Looking to the future

Pulsars and other compact objects probe theories near objects with strong gravitational binding energy. These tests are qualitatively different from Solar-system tests!

WD: 0.01% of mass NS: 10--20% of mass BH: 50% of mass is in binding energy.

Standard profile

Observed profile

Measure offset

Pulsar Timing in a Nutshell

Record the start time of the observation with the observatory clock (typically a maser). The offset gives us a Time of Arrival (TOA) for the observed pulse. Then transform to Solar System Barycentre, enumerate pulses and fit the timing model.

Pulsars available for GR tests

Young pulsars

Recycled pulsars

Equivalence Principle Violations

Pulsar timing can: "  set limits on the Parametrized Post-Newtonian (PPN) parameters α1, α3 (, ζ2) "  test for violations of the Strong Equivalence Principle (SEP) through - the Nordtvedt Effect - dipolar gravitational radiation - variations of Newton's constant (Actually, parameters modified to account for compactness of neutron stars.) (Damour & Esposito-Farèse 1992, CQG, 9, 2093; 1996, PRD, 53, 5541).

SEP: Nordtvedt (Gravitational Stark) Effect

Lunar Laser Ranging: Moon's orbit is not polarized toward Sun.

Constraint: (Williams et al. 2009, IJMPD, 18, 1129)

Binary pulsars: NS and WD fall differently in gravitational field of Galaxy.

Constrain Δnet = ΔNS -ΔWD

(Damour & Schäfer 1991, PRL, 66, 2549.)

WD NS

Result is a polarized orbit.

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η = 4β − γ − 3− 103ξ −α1 +

23α2 −

23ζ1 −

13ζ 2

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η = (4.4 ± 4.5) ×10−4

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Deriving a Constraint on Δnet

Use pulsar—white-dwarf binaries with low eccentricities ( <10-3). Eccentricity would contain a “forced” component along projection of Galactic gravitational force onto the orbit. This may partially cancel “natural” eccentricity.

Constraint ∝ Pb2/e. Need to estimate orbital inclination and masses.

Formerly: assume binary orbit is randomly oriented on sky. Use all similar systems to counter selection effects (Wex). Ensemble of pulsars: Δnet < 9x10-3 (Wex 1997, A&A, 317, 976; 2000, ASP Conf. Ser.).

After Wex 1997, A&A, 317, 976.

Now: use information about longitude of periastron (previously unused) and measured eccentricity and a Bayesian formulation to construct pdfs for Δnet for each appropriate pulsar, representing the full population of similar objects.

Result: |Δnet| < 0.0045 at 95% confidence (Gonzalez et al, submitted, based on method used in Stairs et al. 2005).

Gonzalez et al., submitted.

Constraints on α1 and α3 α1: Implies existence of preferred frames. Expect orbit to be polarized along projection of velocity (wrt CMB) onto orbital plane. Constraint ∝ Pb

1/3/e. Ensemble of pulsars: α1 < 1.4x10-4 (Wex 2000, ASP Conf. Ser.). Comparable to LLR tests (Müller et al. 1996, PRD, 54, R5927).

This test now needs updating with Bayesian approach...

α3: Violates local Lorentz invariance and conservation of momentum. Expect orbit to be polarized, depending on cross-product of system velocity and pulsar spin. Constraint ∝ Pb

2/(eP), same pulsars used as for Δ test. Ensemble of pulsars: α3 < 5.5x10-20 (Gonzalez et al. submitted; slightly worse limit than in Stairs et al. 2005, ApJ, 632, 1060, but more information used). (Cf. Perihelion shifts of Earth and Mercury: ~2x10-7 (Will 1993,

“Theory & Expt. In Grav. Physics,” CUP))

Orbital Decay Tests

These rely on measurement of or constraint on orbital period derivative, . This is complicated by systematic biases:

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Dipolar Gravitational Radiation Difference in gravitational binding energies of NS and WD implies dipolar gravitational radiation possible in, e.g., tensor-scalar theories.

Damour & Esposito-Farèse 1996, PRD, 54, 1474.

Test using pulsar—WD systems in short-period orbits. Examples: PSR B0655+64, 24.7-hour orbit: < 2.7x10-4 (Arzoumanian 2003, ASP Conf. Ser. 302, 69). PSR J1012+5307, 14.5-hour orbit: < 6x10-5 (Lazaridis et al. 2009, MNRAS 400, 805). PSR J0751+1807, 6.3-hour orbit: measurement in Nice et al. 2005 ApJ 634, 1242 has major revision with more data.

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PSR J1141-6545 Young pulsar with a white-dwarf companion, eccentric, 4.45-hour orbit

ω, γ and measured through timing. Sin i measured by scintillation.

Because of eccentricity, dipolar radiation predictions can be large.

Agreement with GR here sets limits of for weakly nonlinear coupling and for strongly nonlinear coupling (Bhat et al 2008, PRD 77, 124017).

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α02 < 2.1×10−5

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˙ P bOrbital decay tests rely on measurement of or constraint on orbital period derivative, .

This is complicated by systematic biases:

Variation of Newton's Constant Spin: Variable G changes moment of inertia of NS. Expect depending on equation of state, PM correction...

Various millisecond pulsars, roughly:

Orbital decay: Expect , test with circular NS-WD binaries.

PSR B1855+09, 12.3-day orbit: (Kaspi, Taylor & Ryba 1994, ApJ, 428, 713; Arzoumanian 1995, PhD thesis, Princeton).

PSR J1713+0747, 67.8-day orbit: (Splaver et al. 2005, ApJ, 620, 405, Nice et al. 2005, ApJ, 634, 1242).

PSR J0437-4715, 5.7-day orbit: (Verbiest et al 2008, ApJ 679, 675, 95% confidence, using slightly different assumptions).

Not as constraining as LLR (Williams et al. 2004, PRL 93, 361101):

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= (4 ± 9) ×10−13 yr−1

Combined Limit on and Dipolar Gravitational Radiation

Lazaridis et al. 2009 (MNRAS 400, 805) combine the limits from J1012+5307 and J0437-4715 to form a combined limit on these two quantities:

and

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T02 / 3M −4 / 3m2 m1 + 2m2( )

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Binary pulsars, especially double-neutron-star systems: measure post-Keplerian timing parameters in a theory-independent way (Damour & Deruelle 1986, AIHP, 44, 263). These predict the stellar masses in any theory of gravity. In GR:

Relativistic Binaries

The Original System: PSR B1913+16

Highly eccentric double-NS system, 8-hour orbit.

The and γ parameters predict the pulsar and companion masses.

The parameter is in good agreement, to ~0.2%. Galactic acceleration modeling now limits this test.

See Weisberg & Taylor 2003, ASP Conf. Ser. 302, 93

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Orbital Decay of PSR B1913+16

See Weisberg, Nice & Taylor, 2010, ApJ 722, 1030

The accumulated shift of periastron passage time, caused by the decay of the orbit. A good match to the predictions of GR!

Mass-mass diagram for the double pulsar J0737-3039A and B. In addition to 5 PK parameters (for A), we measure the mass ratio R. This is independent of gravitational theory ⇒ whole new constraint on gravity compared to other double-NS systems.

As of July 2010; Kramer et al. in prep.

Numbers reported in 2006 (Kramer et al, Science): We can use the measured values of R = 0.9336±0.0005 and = 16.8995±0.0007 o/year to get the masses and then compute the other parameters as expected in GR: Expected in GR: Observed: γ = 0.38418(22) ms γ = 0.3856 ± 0.0026ms = -1.24787(13)×10-12 = (-1.252 ± 0.017)×10-12

r = 6.153(26) ms r = 6.21 ± 0.33 ms

In particular:

This was a 0.05% test of strong-field GR – now down to a ~0.02% test!

Deller et al 2008, Science

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spred= 0.99987 ± 0.00050

Using Multiple Pulsars

Strong constraints on parameters in alternate theories can be achieved by combining information from multiple pulsars plus solar-system tests (Damour & Esposito-Farese).

Geodetic Precession

Precession of either NS's spin axis about the total (~ orbital) angular momentum. Why would we expect this?

Before the second supernova: all AM vectors aligned.

Before the second supernova: all AM vectors aligned.

After second supernova: orbit tilted, misalignment angle δ (shown for recycled A); B spin pointed elsewhere (defined by kick?).

Geodetic Precession Precession period: 300 years for B1913+16, 700 years for B1534+12, 265 years for J1141-6545 and only ~70 years for the J0737-3039 pulsars.

Observed in PSR B1913+16, (Weisberg et al 1989, Kramer 1998)

which will disappear ~2025.

Kramer 1998, ApJ 509, 856

Observed in B1534+12 (Arzoumanian 1995)

and measured by comparison to orbital aberration: o/yr

(68% confidence) cf GR prediction: 0.51 o/yr (Stairs et al 2004, PRL 93, 141101) €

Ω1spin = 0.44−0.16

+0.48

See Kramer 1998, ApJ 509, 856.

What about the double pulsar?

There appear to be no changes in A's profile (Manchester et al 2005, Ferdman et al 2008).

This starts to put strong constraints on the misalignment angle: <37o for one-pole model, <14o for two-pole model (95.4% confidence limits, Ferdman PhD thesis, UBC 2008;

plot updated to 2009).

But B has changed a lot.... and has now disappeared completely!

Perera et al., 2010, ApJ 721, 1193

Dec. 2003

Jan. 2009

McLaughlin et al. 2004a, ApJ 616, L131

B's effects on A provide another avenue to precession:

Eclipses of A by B occur every orbit (Lyne et al 2004, Kaspi et al 2004). A's flux is modulated by the dipolar emission from B.

See Lyutikov & Thompson 2005, ApJ 634, 1223

for a simple geometrical model, illustrated here for April 2007 data by Breton et al. 2008,

Science 321, 104 .

This model makes concrete predictions if B precesses...

Eclipse geometry, Breton et al 2008. If B precesses, ϕ will change with time, and the structure of the eclipse modulation should also change... and it does!

Dec. 2003

Nov. 2007

Courtesy René Breton

Breton et al. 2008, Science 321, 104

The angles α and θ stay constant, but ϕ changes at a rate of 4.77+0.66

-0.65o yr-1. This is

nicely consistent with the rate predicted by GR: 5.0734(7) o yr-1.

And because we measure both orbital semi-major axes, this actually constrains a generalized set of gravitational strong-field theories for the first time! Breton et al. 2008, Science 321, 104

Preferred-frame effects with double-NS systems

Wex & Kramer (2007, MNRAS 380, 455) showed that pulsars similar to the double pulsar are sensitive to preferred-frame effects (within semi-conservative theories) via their orbital parameters. Here they show that the double pulsar (left), a similar system at the Galactic centre (middle) and their combination can lead to strong constraints on the directionality of the preferred frame (PFE antenna).

Future Telescopes The Galactic Census with the Square Kilometre Array should provide: ~30000 pulsars ~1000 millisecond pulsars ~100 relativistic binaries 1—10 pulsar – black-hole systems.

With suitable PSR—BH systems, we may be able to measure the BH spin and quadrupole moment , testing

the Cosmic Censorship conjecture and the No-hair theorem . €

χ ≡cG

SM 2

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q ≡ c 4

G2QM 3

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q = −χ 2

ΔQ/Q = 0.008

Pulsar with 100 μs timing precision in 0.1-year, eccentricity 0.4 orbit around Sgr A*: weekly observations over 3 years lead to a measurement of the spin (via frame-dragging) and quadrupole moment (below) to high precision, assuming Sgr A* is an extreme Kerr BH.

ΔS/S ~ 10-4...10-3

Liu et al., in prep., courtesy Norbert Wex

The challenge will be finding such pulsars!!

Future Prospects

Long-term timing of pulsar – white dwarf systems ⇒ better limits on and dipolar gravitational radiation, as well as PPN-type parameters ⇒ better limits on gravitational-wave background Long-term timing of relativistic systems ⇒ improved tests of strong-field GR. Potential to measure higher-order terms in in 0737A: we may be able to measure the neutron-star moment of inertia! Profile changes and eclipses in relativistic binaries ⇒ better tests of precession rates, geometry determinations. Large-scale surveys, large new telescopes... ⇒ more systems of all types... and maybe some new “holy grails” such as a pulsar—black hole system... stay tuned!

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